Technical Notes - Material Balances in Expansion Type Reservoirs above Bubble Point

One problem of reservoir engineering is the early estimation of the size of newly discovered reservoirs. Often these reservoirs are the expansion type in which sizeable pressure drops occur incident to the production of small fractions of the oil reserve, above the bubble point, and a material balance equation may be solved to find the reserve. The early form of this equation' considered only the compressibility of the oil. Later Hall2 showed that the compressible nature of the formation rock is a significant factor in production above the bubble point, and he presented a new equation which includes a formation (rock) compressibility term. This note presents a further extension of the material balance equation as applied to volumetric, unsat-urated reservoirs above the bubble point by including a term for the presence and compressible nature of the interstitial water. DERIVATION OF EQUATION During a decline in average reservoir pressure, ?p ?p, — p1 the initial reservoir volume V,, will decrease to some value V, due to the reduction in pore volume as a result of a decline in the hydrostatic pressure within the formation, and v, = V,, [l — cr ?p]......(1) The formation compressibility c, is expressed in terms of change in pore volume per unit pore volume per psi. Simultaneously the connate water within the formation expands from an original volume V,, = S,V,, to a new volume V,, V, = s,v,, [I + c,npl.....(2) The difference [Vp — V,] is the hydrocarbon pore volume at pressure p and may be equated to the volume of the remaining oil, or [N — N,] B, = V,,, [I - C~A;] - S,.Vpi [l + cwnjl.........(3) But the initial oil in place in terms of the initial reservoir volume, connate water, and formation volume factor is Ilividing Equation 3 by Equation 4 eliminates V,, to give,